Unformatted text preview: Fig. 2. The path difference between light from adjacent slits in a grating is dsinGl. This calculation gives us the positions of interference minima and maxima on the screen, but not the
intensity as a function of any screen position. That’s a more difficult expression to derive and is done in
many textbooks. For a general N—slit grating, the intensity due to interference effects is given by sin2(Nﬁ)
I 6 = I —— E .4
( ) 0 sin2(B) q
where [3 E gsine Eq. 4a and I0 is the intensity at the central point on the screen. A similar expression for the 2slit case is derived in
Giancoli. See Giancoli also for a plot of intensity as a function of phase and position on screen. Diffraction Effects in Diffraction Gratings To calculate the diffraction pattern caused by the slits, we start by considering just one slit and
using Huygens’ Principle to treat each point along its width as a source of wavelets with the frequency and
phase of the incident plane wave. The net effect on the screen from this slit is the sum of the wavelets from
these point sources. Because of the principle of superposition, we can add up waves in any order we
choose. We ﬁrst add together the wavelets from points A and B in Figure 3, at the top and middle of the DIFFRACTION GRATINGS 4 ...
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 Fall '08
 LIN
 Physics

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